End-point maximal L1 -regularity for the Cauchy problem to a parabolic equation with variable coefficients

Takayoshi Ogawa; Senjo Shimizu

doi:10.1007/s00208-015-1279-8

End-point maximal L¹ -regularity for the Cauchy problem to a parabolic equation with variable coefficients

Takayoshi Ogawa, Senjo Shimizu

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

We consider maximal L¹-regularity for the Cauchy problem to a parabolic equation in the Besov space B˙p,10(Rn) with 1 ≤ p≤ ∞. The estimate obtained here is not available by abstract theory of the class of unconditional martingale differences, because the end-point Besov space is included. We consider the end-point estimate and show that the optimality of maximal regularity in L¹ for the linear parabolic equation with variable coefficients.

Original language	English
Pages (from-to)	661-705
Number of pages	45
Journal	Mathematische Annalen
Volume	365
Issue number	1-2
DOIs	https://doi.org/10.1007/s00208-015-1279-8
Publication status	Published - 2016 Jun 1

Keywords

75C05
Primary 35Q05
Secondary 35L60

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s00208-015-1279-8

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KW - Secondary 35L60

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